Study of Perturbation Designs for the Partially Separable Objective Function With Gradient-Based Optimizations in History Matching

Abstract

Summary Assisted history matching is widely used to constrain reservoir models by integrating well-production data and/or 4D seismic data. However, history matching generally requires a large number of reservoir simulations, which are very CPU time-consuming, in the optimization procedure. In this paper, we present a new technique that allows us to reduce the number of reservoir simulations for the gradient-based optimization method in history matching. The new method is based on the partial separability of the objective function with local components referred to the wells and/or the seismic zones. How to choose a good perturbation design for the gradient computation is the main issue. In this paper, the graph-coloring algorithm is applied to determine “independent” components and parameters for a partially separable function, and analytical test functions are proposed for the selection of perturbation designs. This method can significantly reduce the number of reservoir simulations for a partially separable objective function in history matching.